A Riemann zeta stochastic process

Werner Ehm

doi:10.1016/j.crma.2007.07.023

Probability Theory

A Riemann zeta stochastic process
[Un processus zeta stochastique de Riemann]

Présenté par : Marc Yor

Werner Ehm ¹

¹ Institute for Frontier Areas of Psychology and Mental Health, Wilhelmstr. 3a, 79098 Freiburg, Germany

Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 279-282.

Résumé
Abstract

Il est bien connu que pour tout $σ > 1$ la fonction $t \mapsto ζ (σ + i t) / ζ (σ)$ représente la fonction caractéristique d'une loi de probabilité infiniment divisible. L'objectif de cette Note est de présenter une construction d'un processus aléatoire possédant ces lois marginales. Des théorèmes limite fonctionnels pour ce « processus zeta » et d'autres processus voisins sont indiqués également.

It is well-known that for every $σ > 1$ the function $t \mapsto ζ (σ + i t) / ζ (σ)$ represents the characteristic function of an infinitely divisible probability distribution. The purpose of this Note is to present a construction of a stochastic process having these distributions as its marginals. Functional limit theorems for this ‘zeta process’ and other related processes are also indicated.

Reçu le : 2007-05-11
Accepté le : 2007-07-26
Publié le : 2007-08-22

DOI : 10.1016/j.crma.2007.07.023

Affiliations des auteurs :

Werner Ehm ¹

¹ Institute for Frontier Areas of Psychology and Mental Health, Wilhelmstr. 3a, 79098 Freiburg, Germany

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     title = {A {Riemann} zeta stochastic process},
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     doi = {10.1016/j.crma.2007.07.023},
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Werner Ehm. A Riemann zeta stochastic process. Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 279-282. doi : 10.1016/j.crma.2007.07.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.023/

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